Review: Common Metal Structureshcp ccp (fcc) bcc

ABABABABCABC not close-packed

Features•Filled outer shells spherical atom cores, isotropic bonding•Maximize number of bonds high coordination number•High density

Ionic Bonding & Structures

Which is more stable?

+ –

–

––

–

–

+ –

–

––

–

–

Isotropic bonding; alternate anions and cations

––

–

– –

–+

Just barely stable

http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture3/Lec3.html#anchor4

central atom drawn smaller than available space for clarity

Radius Ratio Rules

CN (cation) Geometry min rc/RA

2 none

(linear)

3 0.155

(trigonal planar)

4 0.225

(tetrahedral)

Consider: CN = 6, 8 12

Octahedral Coordination: CN = 6

2RA

rc + RA

2 2A c AR r R

22

2c A

A

r R

R

2 1 0.414c

A

r

R

rc + RA

2RA

a

Cubic Coordination: CN = 8

2RA

2(rc + RA)

2 AR a

3c A

A

r R

R

3 1 0.732c

A

r

R

a

2( ) 3A cR r a

Cuboctahedral: CN = 12

rc + RA = 2RA

rc = RA rc/RA = 1

2RA

rc + RA

CN Geometry min rc/RA

6 0.414

(octahedral)

8 0.732

(cubic)

12 1

(cuboctahedral)

Radius Ratio Rules

CN (cation) Geometry min rc/RA (f)

2 linear none

3 trigonal planar 0.155

4 tetrahedral 0.225

6 octahedral 0.414

8 cubic 0.732

12 cubo-octahedral 1

if rc is smaller than fRA, then the space is too big and the structure is unstable